Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
A quantum many-body system whose dynamics includes local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions (MPTs) and also to entanglement transitions in random tens...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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American Physical Society
2021
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| _version_ | 1797081456741187584 |
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| author | Nahum, A Roy, S Skinner, B Ruhman, J |
| author_facet | Nahum, A Roy, S Skinner, B Ruhman, J |
| author_sort | Nahum, A |
| collection | OXFORD |
| description | A quantum many-body system whose dynamics includes local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions (MPTs) and also to entanglement transitions in random tensor networks. Many of our results are for “all-to-all” quantum circuits with unitaries and measurements, in which any qubit can couple to any other, and related settings where some of the complications of low-dimensional models are reduced. We also propose field-theory descriptions for spatially local systems of any finite dimensionality. To build intuition, we first solve the simplest “minimal cut” toy model for entanglement dynamics in all-to-all circuits, finding scaling forms and exponents within this approximation. We then show that certain all-to-all measurement circuits allow exact results by exploiting local treelike structure in the circuit geometry. For this reason, we make a detour to give general universal results for entanglement phase transitions in a class of random tree tensor networks with bond dimension 2, making a connection with the classical theory of directed polymers on a tree. We then compare these results with numerics in all-to-all circuits, both for the MPT and for the simpler “forced-measurement phase transition” (FMPT). We characterize the two different phases in all-to-all circuits using observables that are sensitive to the amount of information that is propagated between the initial and final time. We demonstrate signatures of the two phases that can be understood from simple models. Finally we propose Landau-Ginsburg-Wilson-like field theories for the measurement phase transition, the forced-measurement phase transition, and for entanglement transitions in random tensor networks. This analysis shows a surprising difference between the measurement phase transition and the other cases. We discuss variants of the measurement problem with additional structure (for example free-fermion structure), and questions for the future. |
| first_indexed | 2024-03-07T01:14:37Z |
| format | Journal article |
| id | oxford-uuid:8e39cb41-db6a-492c-b0ea-d0684a4ba6db |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:14:37Z |
| publishDate | 2021 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:8e39cb41-db6a-492c-b0ea-d0684a4ba6db2022-03-26T22:56:15ZMeasurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8e39cb41-db6a-492c-b0ea-d0684a4ba6dbEnglishSymplectic ElementsAmerican Physical Society2021Nahum, ARoy, SSkinner, BRuhman, JA quantum many-body system whose dynamics includes local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions (MPTs) and also to entanglement transitions in random tensor networks. Many of our results are for “all-to-all” quantum circuits with unitaries and measurements, in which any qubit can couple to any other, and related settings where some of the complications of low-dimensional models are reduced. We also propose field-theory descriptions for spatially local systems of any finite dimensionality. To build intuition, we first solve the simplest “minimal cut” toy model for entanglement dynamics in all-to-all circuits, finding scaling forms and exponents within this approximation. We then show that certain all-to-all measurement circuits allow exact results by exploiting local treelike structure in the circuit geometry. For this reason, we make a detour to give general universal results for entanglement phase transitions in a class of random tree tensor networks with bond dimension 2, making a connection with the classical theory of directed polymers on a tree. We then compare these results with numerics in all-to-all circuits, both for the MPT and for the simpler “forced-measurement phase transition” (FMPT). We characterize the two different phases in all-to-all circuits using observables that are sensitive to the amount of information that is propagated between the initial and final time. We demonstrate signatures of the two phases that can be understood from simple models. Finally we propose Landau-Ginsburg-Wilson-like field theories for the measurement phase transition, the forced-measurement phase transition, and for entanglement transitions in random tensor networks. This analysis shows a surprising difference between the measurement phase transition and the other cases. We discuss variants of the measurement problem with additional structure (for example free-fermion structure), and questions for the future. |
| spellingShingle | Nahum, A Roy, S Skinner, B Ruhman, J Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory |
| title | Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory |
| title_full | Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory |
| title_fullStr | Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory |
| title_full_unstemmed | Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory |
| title_short | Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory |
| title_sort | measurement and entanglement phase transitions in all to all quantum circuits on quantum trees and in landau ginsburg theory |
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